Arrange the following in decreasing order of oxidation state of the underlined element:
$\text{N}_2\underline{\text{O}}_5$, $\text{Al}_2\underline{\text{O}}_3$, $\text{H}_2\underline{\text{S}}$

The concept of oxidation state (or oxidation number) is one of the most fundamental in chemistry, providing a systematic bookkeeping tool for tracking the distribution of electrons in chemical compounds and for understanding and balancing redox reactions. Oxidation state is a formal charge assigned to an atom in a compound based on a set of rules that assume ionic character in all bonds. The assignment rules, in order of priority: Fluorine is always -1 (most electronegative element, never +). Hydrogen is +1 in most compounds (exception: -1 in metal hydrides like NaH, CaH2, LiAlH4). Oxygen is -2 in most compounds (exceptions: -1 in peroxides H2O2, Na2O2, BaO2; -1/2 in superoxides like KO2; +2 in OF2; +1 in O2F2). Halogens Cl, Br, I: -1 in most compounds; can be positive when bonded to more electronegative O or F (e.g., Cl = +5 in ClO3-, Cl = +7 in ClO4-, I = +5 in IO3-). Sum rule: the sum of oxidation states of all atoms in a neutral compound = 0; the sum in a polyatomic ion = the charge of the ion. For monatomic ions: oxidation state = charge (Na+ = +1, Fe3+ = +3, S2- = -2, N3- = -3). For elements in their standard state (pure element): oxidation state = 0 (Na, Fe, S8, N2, O2, Cl2 all have oxidation state = 0).

Redox (reduction-oxidation) reactions involve the transfer of electrons between chemical species. The species that loses electrons is oxidised (its oxidation state increases); the species that gains electrons is reduced (its oxidation state decreases). Mnemonics: OIL RIG (Oxidation Is Loss, Reduction Is Gain of electrons) or LEO GER (Lose Electrons Oxidation, Gain Electrons Reduction). For every redox reaction, the increase in oxidation state of the oxidised species exactly equals the decrease in oxidation state of the reduced species (electron transfer is conserved). Balancing redox equations: Half-reaction method (most systematic): (1) Write the unbalanced skeleton equation. (2) Separate into two half-reactions (oxidation and reduction). (3) Balance each half-reaction for atoms (except H and O). (4) Balance O by adding H2O; balance H by adding H+. (5) Balance charge by adding electrons. (6) Multiply half-reactions to make electron transfer equal. (7) Add the half-reactions and cancel species that appear on both sides. In alkaline medium: same procedure, then add OH- to both sides to convert H+ to H2O. This systematic method works for all redox equations, however complex.

Strong oxidising agents (electron acceptors, easy to reduce): F2 (strongest oxidising agent, E° = +2.87 V), O3 (ozone, +2.07 V), H2O2 (+1.77 V in acid), MnO4- (permanganate, +1.51 V in acid), Cl2 (+1.36 V), Cr2O7^2- (dichromate, +1.33 V in acid), HNO3 (conc., +0.96 V), Br2 (+1.07 V), O2 (+1.23 V in acid), I2 (+0.54 V). Strong reducing agents (electron donors, easy to oxidise, most negative E°): Li (-3.04 V), Ca (-2.87 V), Na (-2.71 V), Mg (-2.36 V), Al (-1.67 V), Zn (-0.76 V), Fe (-0.44 V), H2 (0.00 V reference). Among non-metals: S2- (in H2S), I-, Sn2+, Fe2+, SO2, C (carbon as coke in metallurgy), CO (carbon monoxide in blast furnace). Specific reducing agents in organic chemistry: NaBH4 (reduces aldehydes and ketones to alcohols, mild — does not reduce carboxylic acids or esters under normal conditions). LiAlH4 (strong reducing agent — reduces all carbonyl compounds including carboxylic acids, esters, amides, nitriles to alcohols/amines).

Disproportionation (also called auto-oxidation or self-redox) is a redox reaction in which a single species in one oxidation state is simultaneously oxidised to a higher state AND reduced to a lower state — the substance reacts with itself. Examples: Cl2 + 2NaOH → NaCl + NaOCl + H2O: Cl2 has Cl at 0; products have Cl at -1 (NaCl) and +1 (NaOCl) — disproportionation at 0 → -1 and +1. H2O2 → H2O + O2: O goes from -1 → -2 and 0. P4 + 3NaOH + 3H2O → PH3 + 3NaH2PO2: P(0) → P(-3) in PH3 and P(+1) in hypophosphite. 2Cu+ → Cu + Cu2+ (in acidic aqueous solution): Cu(+1) → Cu(0) and Cu(+2). Comproportionation (synproportionation) is the reverse — two species in different oxidation states react to give a single intermediate oxidation state product: Cu + Cu2+ → 2Cu+ (in the presence of appropriate ligands). S^0 + SO4^2- → S2O3^2- (in some reactions). These reactions are important in analytical chemistry (stability of intermediates) and in preparative chemistry (synthesis of compounds in intermediate oxidation states).

Nitrogen forms one of the richest and most diverse chemistries of any element, exhibiting stable compounds in virtually every integer oxidation state from -3 to +5. The nitrogen oxides and their chemistry are particularly important for both industrial applications and environmental concerns. N2O (dinitrogen oxide, nitrous oxide, "laughing gas", N = +1): used as an anaesthetic and as a propellant in food aerosol cans (cream dispensers). Produced by gentle heating of ammonium nitrate: NH4NO3 → N2O + 2H2O. NO (nitric oxide, N = +2): colourless gas, physiological signalling molecule (vasodilator, neurotransmitter), produced in combustion engines and lightning. Oxidised by O2 to NO2. Produced industrially: 4NH3 + 5O2 → 4NO + 6H2O (Ostwald process, Pt catalyst, 850°C). NO2 (nitrogen dioxide, N = +4): brown gas, toxic, involved in photochemical smog and acid rain: 2NO2 + H2O → HNO3 + HNO2. N2O5 (dinitrogen pentaoxide, N = +5): white solid, anhydride of nitric acid. Unstable, decomposes slowly. Reacts vigorously with water: N2O5 + H2O → 2HNO3. HNO3 (nitric acid, N = +5): made by Ostwald process (NO → NO2 → HNO3). Strong oxidising acid used in manufacture of fertilisers (ammonium nitrate, NH4NO3), explosives (TNT, RDX, nitroglycerin), dyes, and pharmaceuticals. Concentrated HNO3 passivates Fe, Cr, Al by forming protective oxide layer.

Sulfur exhibits oxidation states ranging from -2 to +6, making it one of the elements with the widest range of stable oxidation states. H2S (S = -2): toxic gas with rotten egg smell, weak diprotic acid (pKa1 = 7, pKa2 = 12.9), reducing agent, formed in volcanic emissions and decay of organic sulfur compounds. Elemental sulfur S8 (S = 0): yellow solid, rhombic allotrope most stable below 96°C, monoclinic above; used in vulcanisation of rubber, manufacture of H2SO4, pesticides, and matches. SO2 (S = +4): colourless gas with pungent smell, formed in combustion of S-containing fuels and in roasting of sulfide ores; weak acid in water (sulfurous acid H2SO3, pKa = 1.8); used as food preservative (E220), bleaching agent (for wool and straw), and in paper manufacturing; major air pollutant contributing to acid rain (SO2 + H2O → H2SO3 → H+ + HSO3-, then further to H2SO4). SO3 (S = +6): made from SO2 by catalytic oxidation (Contact process, V2O5 catalyst): 2SO2 + O2 → 2SO3. Reacts with water to form H2SO4: SO3 + H2O → H2SO4. H2SO4 (S = +6): most important industrial chemical, produced by Contact process (45 million tonnes/year globally). Properties: highly corrosive, dehydrating agent, strong diprotic acid, oxidising agent (hot concentrated). Uses: production of fertilisers (ammonium sulfate, superphosphate), chemical synthesis (HCl, HNO3, HF), petroleum refining, lead-acid batteries, cleaning of metals. Sodium thiosulfate Na2S2O3 (average S = +2, but one S is -1 and one is +5 by structure): used as photographic fixer (dissolves AgBr), antidote to cyanide poisoning (thiosulfate converts CN- to less toxic thiocyanate), and to standardise I2 solutions (2S2O3^2- + I2 → S4O6^2- + 2I-).